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A140144
a(1)=1, a(n)=a(n-1)+n^1 if n odd, a(n)=a(n-1)+ n^0 if n is even.
3
1, 2, 5, 6, 11, 12, 19, 20, 29, 30, 41, 42, 55, 56, 71, 72, 89, 90, 109, 110, 131, 132, 155, 156, 181, 182, 209, 210, 239, 240, 271, 272, 305, 306, 341, 342, 379, 380, 419, 420, 461, 462, 505, 506, 551, 552, 599, 600, 649, 650, 701, 702, 755, 756, 811, 812, 869
OFFSET
1,2
COMMENTS
Equals triangle A177990 * [1,2,3,...]. - Gary W. Adamson, May 16 2010
FORMULA
From R. J. Mathar, Feb 22 2009: (Start)
a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5).
G.f.: x*(-1-x-x^2+x^3)/ ((1+x)^2*(x-1)^3). (End)
a(n) = Sum_{k=1..n} k^(k mod 2). - Wesley Ivan Hurt, Nov 20 2021
MATHEMATICA
a = {}; r = 1; s = 0; Do[k = 0; Do[k = k + (Sin[Pi m/2]^2) m^r + (Cos[Pi m/2]^2) m^s, {m, 1, n}]; AppendTo[a, k], {n, 1, 100}]; a
CROSSREFS
Cf. A177990. - Gary W. Adamson, May 16 2010
Cf. A002378 (even bisection), A028387 (odd bisection).
Sequence in context: A057812 A329572 A329569 * A328893 A030130 A164874
KEYWORD
nonn,easy
AUTHOR
Artur Jasinski, May 12 2008
STATUS
approved